333 research outputs found
Non-hermitean delocalization in an array of wells with variable-range widths
Nonhermitean hamiltonians of convection-diffusion type occur in the
description of vortex motion in the presence of a tilted magnetic field as well
as in models of driven population dynamics. We study such hamiltonians in the
case of rectangular barriers of variable size. We determine Lyapunov exponent
and wavenumber of the eigenfunctions within an adiabatic approach, allowing to
reduce the original d=2 phase space to a d=1 attractor. PACS
numbers:05.70.Ln,72.15Rn,74.60.GeComment: 20 pages,10 figure
Reaction-diffusion systems and nonlinear waves
The authors investigate the solution of a nonlinear reaction-diffusion
equation connected with nonlinear waves. The equation discussed is more general
than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results
are presented in a compact and elegant form in terms of Mittag-Leffler
functions and generalized Mittag-Leffler functions, which are suitable for
numerical computation. The importance of the derived results lies in the fact
that numerous results on fractional reaction, fractional diffusion, anomalous
diffusion problems, and fractional telegraph equations scattered in the
literature can be derived, as special cases, of the results investigated in
this article.Comment: LaTeX, 16 pages, corrected typo
Solution of generalized fractional reaction-diffusion equations
This paper deals with the investigation of a closed form solution of a
generalized fractional reaction-diffusion equation. The solution of the
proposed problem is developed in a compact form in terms of the H-function by
the application of direct and inverse Laplace and Fourier transforms.
Fractional order moments and the asymptotic expansion of the solution are also
obtained.Comment: LaTeX, 18 pages, corrected typo
Plasmon-pole approximation for semiconductor quantum wire electrons
We develop the plasmon-pole approximation for an interacting electron gas
confined in a semiconductor quantum wire. We argue that the plasmon-pole
approximation becomes a more accurate approach in quantum wire systems than in
higher dimensional systems because of severe phase-space restrictions on
particle-hole excitations in one dimension. As examples, we use the
plasmon-pole approximation to calculate the electron self-energy due to the
Coulomb interaction and the hot-electron energy relaxation rate due to
LO-phonon emission in GaAs quantum wires. We find that the plasmon-pole
approximation works extremely well as compared with more complete many-body
calculations.Comment: 16 pages, RevTex, figures included. Also available at
http://www-cmg.physics.umd.edu/~lzheng
Fractional reaction-diffusion equations
In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b)
derived solutions of a number of fractional kinetic equations in terms of
generalized Mittag-Leffler functions which provide the extension of the work of
Haubold and Mathai (1995, 2000). The subject of the present paper is to
investigate the solution of a fractional reaction-diffusion equation. The
results derived are of general nature and include the results reported earlier
by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for
anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for
reaction-diffusion systems with L\'evy flights. The solution has been developed
in terms of the H-function in a compact form with the help of Laplace and
Fourier transforms. Most of the results obtained are in a form suitable for
numerical computation.Comment: LaTeX, 17 pages, corrected typo
Magnetoresistance of Two-Dimensional Fermions in a Random Magnetic Field
We perform a semiclassical calculation of the magnetoresistance of spinless
two-dimensional fermions in a long-range correlated random magnetic field. In
the regime relevant for the problem of the half filled Landau level the
perturbative Born approximation fails and we develop a new method of solving
the Boltzmann equation beyond the relaxation time approximation. In absence of
interactions, electron density modulations, in-plane fields, and Fermi surface
anisotropy we obtain a quadratic negative magnetoresistance in the weak field
limit.Comment: 12 pages, Latex, no figures, Nordita repor
Thermodynamic properties of the d-density wave order in cuprates
We solve a popular effective Hamiltonian of competing -density wave and
d-wave superconductivity orders self-consistently at the mean-field level for a
wide range of doping and temperature. The theory predicts a temperature
dependence of the -density wave order parameter seemingly inconsistent with
the neutron scattering and SR experiments of the cuprates. We further
calculate thermodynamic quantities, such as chemical potential, entropy and
specific heat. Their distinct features can be used to test the existence of the
-density wave order in cuprates.Comment: changed to 4 pages and 4 figures. More reference added. Accepted by
Phys. Rev.
Polarization properties of four-wave mixing in strained semiconductor optical amplifiers
Spinless particle in rapidly fluctuating random magnetic field
We study a two-dimensional spinless particle in a disordered gaussian
magnetic field with short time fluctuations, by means of the evolution equation
for the density matrix ; in this
description the two coordinates are associated with the retarded and advanced
paths respectively. The static part of the vector potential correlator is
assumed to grow with distance with a power ; the case corresponds to
a -correlated magnetic field, and to free massless field. The
value separates two different regimes, diffusion and logarithmic growth
respectively. When the baricentric coordinate diffuses with a coefficient proportional to , where
is the relative coordinate: . As the
correlator of the magnetic field is a power of distance with positive exponent;
then the coefficient scales as .
The density matrix is a function of and ,and its width in
grows for large times proportionally to .Comment: latex2e; 2 figure
Ballistic electron motion in a random magnetic field
Using a new scheme of the derivation of the non-linear -model we
consider the electron motion in a random magnetic field (RMF) in two
dimensions. The derivation is based on writing quasiclassical equations and
representing their solutions in terms of a functional integral over
supermatrices with the constraint . Contrary to the standard scheme,
neither singling out slow modes nor saddle-point approximation are used. The
-model obtained is applicable at the length scale down to the electron
wavelength. We show that this model differs from the model with a random
potential (RP).However, after averaging over fluctuations in the Lyapunov
region the standard -model is obtained leading to the conventional
localization behavior.Comment: 10 pages, no figures, to be submitted in PRB v2: Section IV is
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